"""
Problem 42: https://projecteuler.net/problem=42

The nth term of the sequence of triangle numbers is given by, tn = ½n(n+1); so
the first ten triangle numbers are:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

By converting each letter in a word to a number corresponding to its
alphabetical position and adding these values we form a word value. For example,
the word value for SKY is 19 + 11 + 25 = 55 = t10. If the word value is a
triangle number then we shall call the word a triangle word.

Using words.txt (right click and 'Save Link/Target As...'), a 16K text file
containing nearly two-thousand common English words, how many are triangle
words?
"""

# _*_ conding:UTF-8 _*_
'''
@author = Kuperain
@email = kuperain@aliyun.com
@IDE = VSCODE Python3.8.3
@creat_time = 2022/5/14                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
'''

LetterDict = {chr(x): x-ord('a') + 1
              for x in range(ord('a'), ord('z')+1)}
LetterDict.update({chr(x): x-ord('A')+1
                   for x in range(ord('A'), ord('Z')+1)})

Trianglenumbers = [n*(n+1)//2 for n in range(50)]


def solution(input: str = 'p042_words.txt') -> int:
    with open(input, 'r') as fp:
        names = eval('['+fp.read().strip()+']')

    def isTriangleword(name: str) -> int:
        value = 0
        for c in name:
            if c not in LetterDict:  # special chars, such as '-','.'
                LetterDict[c] = ord(c.lower()) - ord('a')+1
            value += LetterDict[c]

        return value in Trianglenumbers or (
            int((8*value+1)**0.5)**2 == 8*value+1)
        # solve equation n(n+1) = 2value

    return sum(list(map(isTriangleword, names)))


if __name__ == "__main__":
    import doctest
    doctest.testmod(verbose=False)

    print(solution())
    # 162
